Influence of Perturbations of Fuel Inner Surface of Cryogenic Target on its Burning

The central question for laser ICF problem is symmetrical compression of the target. Today the active discussio ns and experimental studies on laser facilities are concentrated on two type of laser targets – so called direct and indirect drive targets [1-4]. Now new more powerful laser facilities as NIF [5], LMJ [6] and ISKRA-6 [7] are being under construction. It is supposed that the power of this facilities is sufficient to achieve burning of the thermonuclear fuel in ICF experiments. The choice of optimal target design is very complicated and multi parametric problem. There are many factors that can have effect on design. The desire for achievement maximum thermonuclear energy at minimum laser energy applies rigid requirements on laser pulse profile and its agreement with target parameters (mass, diameter, thickness etc.). It depends on the type of compression scheme. But for both type of compression the hydrodynamic flow is unstable. So initial perturbations will be grow during two stage when the target shell will be accelerated by rare targets corona and then during deceleration by fuel. Initial perturbation spectra are formed both due to irradiation non uniformities and due to shell non uniformities which originates during target fabrication. We performed the analysis of one mode spherical harmonic perturbation growth. Th